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A limping knight on a chessboard

Source: Baltic Way 2017, Problem 8

November 26, 2017
combinatoricscombinatorics proposedChess knightChessboard

Problem Statement

A chess knight has injured his leg and is limping. He alternates between a normal move and a short move where he moves to any diagonally neighbouring cell. The limping knight moves on a 5×65 \times 6 cell chessboard starting with a normal move. What is the largest number of moves he can make if he is starting from a cell of his own choice and is not allowed to visit any cell (including the initial cell) more than once?